Adding
Adding fractions is really simple. First you have to find the lowest common denominator (the lowest number that both denominators go into), then add both numerators using the lowest common denominator. If it is a mixed fraction, you convert it to a improper fraction. To convert it, you multiply the denominator with the whole number, then add the numerator. You then place that number over the numerator; the improper fraction should have a numerator that is larger than the denominator, hence the name improper fraction. Alternatively, you can add the whole numbers, and simply add the fractions, then you put both of them together. This way is recommended when adding, it is a lot simpler.
Subtracting
Subtracting fractions is almost just as simple. Instead of adding, you subtract. You find the lowest common denominator and subtract the numerators, and often, you simplify at the end. If it is a mixed fraction, subtract the whole numbers, and fractions, if possible. If it isn't possible to subtract the fractions, subtract one, from the first mixed number, then add the numerator and denominator, and use the sum of that to replace the first numerator in the fraction; now it is a improper fraction. Finally, subtract normally.
Dividing
Probably the most confusing of all, is division. There are two ways to divide, using a ratio table, or using the reciprocal, the ratio table is easier in my opinion. To use the ratio table, we place the fraction that is being divided on the left side of the table, and the divisor fraction on the right side of the table. Here, we focus mostly on the divisor fraction. Using division and multiplication, make that divisor fraction into a whole. What you do to the divisor fraction, you must do to the fraction that is being divided. Your answer will be the results of the fraction being divided. To use the reciprocal, all you do is turn the second fraction upside down, and multiply.
Multiplication
Multiplying fractions is a bit easier. You simply multiply the numerators and denominators, then simplify. To multiply mixed numbers, convert them to improper fractions, then multiply, then convert them back to mixed numbers.
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